Find the surface area of the cone in terms of pie

Answer:

4[tex]x^{3}[/tex] - 16[tex]x^{2}[/tex] + 15x

Step-by-step explanation:

length = 5 - 2x

width = 3 - 2x

heighth = x

x(5 - 2x)(3 - 2x)

x(15 -16x + 4[tex]x^{2}[/tex])

4[tex]x^{3}[/tex] - 16[tex]x^{2}[/tex] + 15x

The largest volume of such a box is 4.345[tex]ft^{3}[/tex].

Given that,

A rectangular sheet of cardboard 3 feet by 5 feet will be made into an open box by cutting equal-sized squares from each corner and folding up the four edges.

The shaded region represents the area  that was cut from the corners of the box.

We have to determine,

The largest volume of such a box.

According to the question,

The height will be  x

The width will be  (3 − 2 x)

And the length will be ( 5− 2 x)

.

The formula for volume will be,

[tex]Volume = Length \times Height \times Width\\\\[/tex]

Substitute the values in the formula,

[tex]Volume = x(3-2x).(5-2x)\\\\Volume = (3x-6x^{2}).(5-2x)\\\\Volume = 3x(5-2x) - 6x^{2}(5-2x)\\\\Volume = 15x - 6x^{2} - 30x^{2} + 12x^{3}\\\\Volume = 12x^{3} -36x^{2} + 15x[/tex]

 Then,

To Find the derivative of the equation,

[tex]V = 12x^{3} -36x^{2} + 15x\\\\Differentiate\ with\ respect\ to\ x\ both\ sides,\\\\\dfrac{dv}{dx} = \dfrac{d(12x^{3} -36x^{2} + 15x)}{dx}\\\\V' = 36x^{2} - 72x+15[/tex]

The critical numbers by seeing where  V '  =  0,

[tex]= 36x^{2} -72x +15\\\\= 3 ( 12x^{2} - 24x +5 )\\[/tex]

By using the quadratic formula or your calculator to solve for  

x = 0.23, and 1.6

x = 1.6 is not in the domain since that would make one of our side lengths less than zero.  x  =  0.23

Plug x back into the equations to get the dimensions,

[tex]3-2x = 3- 2 \times -0.23 = 3+0.46 = 3.46\\5-2x = 5 - 2 \times -0.23 = 5+0.46 = 5.46[/tex]

Therefore, the dimension are  0.23 ft x 3.46 ft x  5.46 ft.

Hence, The largest volume of such a box is 4.345[tex]ft^{3}[/tex].

To know more about Dimension click the link given below.

https://brainly.com/question/23288467

Answer:

y=15

Step-by-step explanation:

y=21 - 6

y = 15

hope this helped!

Answer:

The mean of Trail Middle School wrestling team is greater by 20 pounds as compared to that of Burlington Middle School  wrestling team

Step-by-step explanation:

Since the value of absolute deviation in case of Trail Middle School wrestling team and Burlington Middle School  wrestling team is same. Hence, there will be no impact of it while determining the difference in mean deviation of both the team.

Thus, the difference in mean deviation is [tex]150-130 = 20[/tex]

The mean of Trail Middle School wrestling team is greater by 20 pounds as compared to that of Burlington Middle School  wrestling team

Answer:

9.42 cubic inches

Step-by-step explanation:

We are to find the volume of the cone.

The formula is given as:

1/3πr²h

From the question,

Diameter = 3 inches, Radius = D/2 = 3/2

r = 1.5 inches

h = 4 inches

Hence, the volume of the cone =

1/3 × π × 1.5² × 4

= 9.42 cubic inches

Therefore, the filter can hold 9.42 cubic inches of liquid without overflowing.

y=5x-3 I think so.....

Answer:

1. m<a and m<h, m<e and m<d

2.m<a and m<c, m<b and m<d, m<e and m<g, m<f and m<h

3. m<a= 112

m<c=112

m<f=112

m<h=112

m<b=68

m<d=68

m<e=68

m<g=68

Hello !

Answer:

[tex]\large\boxed{\sf Option\ 3 : 66cm}[/tex]

Step-by-step explanation:

The circumference of a circle is given by [tex]\sf C=2\times\pi\times r[/tex], where r is the radius.

Given :

Let's replace r with its value in the previous formula :

[tex]\sf C=2\times 3.14\times 10.5[/tex]

[tex]\sf C=65.94[/tex]

[tex]\boxed{\sf C\approx 66cm}[/tex]

Have a nice day

Answer:

3

Step-by-step explanation:

Considering she wore a black shirt 6 times in 20 days will give you the statistic of 3/10. If the question is about the next 10 days then she will wear 3 black shirts. (It's also 1/2 of the original question.)

Answer:

21 hours

Step-by-step explanation:

After 2 hours the temperature has risen to 7°f

The time taken to rise to an additional 13°f can be calculated as follows

1 hour takes 3.5°f

13°f = 3.5×6

= 21 hours

Hence it would take 21 hours

Answer:

-1.5

Step-by-step explanation:

5x6=30

30-21=9

9/6=1.5

remember tht the answer is NEGATIVE,, thnk u hav a good nite

Answer:

x=6

Step-by-step explanation:

30=6+4x

you have to combine the number that are the same, like 2 and 4 or 3x and 4x

30-6=4x (you should always remember when you move a number if it was - it will turn +)

30-6=4x

24=4x

x=24/4

x=6

Answer: y=36^(2)x*49

Step-by-step explanation: Graph.

Brainliest or a thank you if im right please :)) <3

Answer: either I don't understand the question or its 72% and I'm fairly certain its 72%

Answer: n=-5/12

Step-by-step explanation: 1/3-3/4=-5/12

hoped this helped :))

Answer: n= 5/12

Step-by-step explanation: 13=+3413=n+3431​=n+43​13−34=+34−34

Hope this helps!

Answer:

13 is c

14 is b

Step-by-step explanation:

Answer:

4(x-5)= 4x-20

so the equivalent equation is 4(x-5)

Answer:

I don't actually know sorry

Step-by-step explanation:

I don't know

Answer:

B

Step-by-step explanation:

Answer:

it's 0.625

Step-by-step explanation:

Answer:

Boys: 2/17

Girls: 4/17

Step-by-step explanation:

2 + 15 = 17 (to get the total number of boys in Sapphire's class)

4 + 13 = 17 (to get the total number of girls in the class)

The proportion is how many who are left handed over the total number of girls/boys. ^^

So, left-handed for boys = 2, which makes the proportion 2/17

And there are 4 left-handed girls, so the proportion is 4/17

Answer:

3.43%

Step-by-step explanation:

362-350=12

12:350*100 =

(12*100):350 =

1200:350 = 3.43

Answer:

9

Step-by-step explanation:

radius is half of the diameter

Answer:

Perpendicular

Step-by-step explanation:

Answer:

4%

Step-by-step explanation:

Given data

The total sales= $8900

Donated amount=$356

Hence the percent donated is

=Donated amount/Total Sales *100

= 356/8900*100

=0.04*100

=4%

Hence the donated percent is 4%

Answer:

45 degrees

Step-by-step explanation:

The following shape is an octagon, having 8 sides and knowing that any regular polygon has an exterior angle value of 360 degrees, you can say 360/8 to find the measure of each exterior angle, leading to equal 45 degrees.

Hope it helped! (:

Answer:

x=4-√79, x=4+√79

Step-by-step explanation:

Answer:

457.9

Step-by-step explanation:

Answer:

(1,3)

Step-by-step explanation:

Linear equations are typically organized in slope-intercept form: [tex]y=mx+b[/tex] where m is the slope and b is the y-intercept (the value of y when the line crosses the y-axis, or when x is equal to 0).

We're given that this line contains the point (0,1). This tells us that the y-intercept (b) of the line is 1.  We're also given that this line has a slope (m) of 2. Plug these values into [tex]y=mx+b[/tex]:

[tex]y=2x+1[/tex]

Now, plug in all of the possible points to see which are solutions.

1) (1,3)

[tex]3=2(1)+1\\3=2+1\\3=3[/tex]

Because the left side of the equation is equal to the right, (1,3) also lies on this line.

2) (3,1)

[tex]1=2(3)+1\\1=6+1\\1=7[/tex]

Because the left side is not equal to the right, (3,1) does not lie on the line.

3) (2,2)

[tex]2=2(2)+1\\2=4+1\\2=5[/tex]

Because the left side is not equal to the right, (2,2) does not lie on the line.

4) (2,3)

[tex]3=2(2)+1\\3=4+1\\3=5[/tex]

Because the left side is not equal to the right, (2,3) does not lie on the line.

I hope this helps!

Answer:

m<A=97

m<B=97

Step-by-step explanation:

m<A=m<B

Congruent angles and they are vertical angles. The other two are also the same because the angles given have the same degrees.

m<A is supplementary to 83 degrees

Supplementary angles are two angles that sum up to 180 degrees.

180-83=97

97 degrees is the answer for each missing angles.